Elliptic curve isogeny class with Cremona label 47040ep (LMFDB label 47040.e)

• Label: 47040ep
• Number of curves: $4$
• Conductor: $47040$
• CM: no
• Rank: $1$

Elliptic curves in class 47040ep

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47040.e3	47040ep1	\([0, -1, 0, -13981, -605219]\)	\(2508888064/118125\)	\(14230823040000\)	\([2]\)	\(147456\)	\(1.2847\)	\(\Gamma_0(N)\)-optimal
47040.e2	47040ep2	\([0, -1, 0, -38481, 2124081]\)	\(3269383504/893025\)	\(1721360354918400\)	\([2, 2]\)	\(294912\)	\(1.6312\)
47040.e4	47040ep3	\([0, -1, 0, 98719, 13731201]\)	\(13799183324/18600435\)	\(-143413908426915840\)	\([2]\)	\(589824\)	\(1.9778\)
47040.e1	47040ep4	\([0, -1, 0, -567681, 164800161]\)	\(2624033547076/324135\)	\(2499160218992640\)	\([2]\)	\(589824\)	\(1.9778\)

Rank

The elliptic curves in class 47040ep have rank \(1\).

Complex multiplication

The elliptic curves in class 47040ep do not have complex multiplication.

Modular form 47040.2.a.ep

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.